It is frequently necessary to carry a large number of such workpieces in quick succession over a predetermined path, e.g. from a stack of such workpieces to a conveyor serving to separate them from one another. For a rapid transfer from a loading station to an unloading station, two transport units may be used, one of which picks up a workpiece at the loading station and carries it to the unloading station while the other, having released a previously engaged workpiece at that unloading station, returns empty to the loading station for another pickup. If it is desired to let the transport units travel back and forth along the shortest path, the problem arises of avoiding collisions therebetween and providing enough clearance so that the returning idle transport unit will not interfere with the oncoming working unit and its load.